The Stochastic Container Relocation Problem

The Container Relocation Problem (CRP) is concerned with finding a sequence of moves of containers that minimizes the number of relocations needed to retrieve all containers, while respecting a given order of retrieval. However, the assumption of knowing the full retrieval order of containers is particularly unrealistic in real operations. This paper studies the stochastic CRP (SCRP), which relaxes this assumption. A new multi-stage stochastic model, called the batch model, is introduced, motivated, and compared with an existing model (the online model). The two main contributions are an optimal algorithm called Pruning-Best-First-Search (PBFS) and a randomized approximate algorithm called PBFS-Approximate with a bounded average error. Both algorithms, applicable in the batch and online models, are based on a new family of lower bounds for which we show some theoretical properties. Moreover, we introduce two new heuristics outperforming the best existing heuristics. Algorithms, bounds and heuristics are tested in an extensive computational section. Finally, based on strong computational evidence, we conjecture the optimality of the “Leveling” heuristic in a special “no information” case, where at any retrieval stage, any of the remaining containers is equally likely to be retrieved next

Sea Container Terminals

Due to a rapid growth in world trade and a huge increase in containerized goods, sea container terminals play a vital role in globe-spanning supply chains. Container terminals should be able to handle large ships, with large call sizes within the shortest time possible, and at competitive rates. In response, terminal operators, shipping liners, and port authorities are investing in new technologies to improve container handling infrastructure and operational efficiency. Container terminals face challenging research problems which have received much attention from the academic community. The focus of this paper is to highlight the recent developments in the container terminals, which can be categorized into three areas: (1) innovative container terminal technologies, (2) new OR directions and models for existing research areas, and (3) emerging areas in container terminal research. By choosing this focus, we complement existing reviews on container terminal operations

An Improved Fuzzy Knowledge-Based Model For Long Stay Container Yards

This paper considers the problem of allocating newly arrived containers to stacks of existing containers in a yard when the departure date/time for containers is unknown. Many factors and constraints need to be considered when modelling this storage allocation problem. These constraints include the size, type and weight of the containers. The factors are the number of containers in a stack and the duration of stay of the topmost container in the stack. This paper aims to develop an improved Fuzzy Knowledge-Based ‘FKB’ model for best allocation practice of long-stay containers in a yard. In this model, the duration of stay factor does not need to be considered in the allocation decision if the duration of stay for the topmost containers in a stack is similar; hence, a new ‘ON/OFF’ strategy is proposed within the Fuzzy Knowledge-Based model to activate/deactivate this factor in the stacking algorithm whenever is required. Discrete Event Simulation and Fuzzy Knowledge-Based techniques are used to develop the proposed model. The model’s behaviour is tested using three real-life scenarios, including allocating containers in busy, moderately busy and quiet yards. The total number of re-handlings, the number of re-handlings per stack, and the number of re-handlings for containers were considered KPIs in each scenario

Research into container reshuffling and stacking problems in container terminal yards

Container stacking and reshuffling are important issues in the management of operations in a container terminal. Minimizing the number of reshuffles can increase productivity of the yard cranes and the efficiency of the terminal. In this research, the authors improve the existing static reshuffling model, develop five effective heuristics, and analyze the performance of these algorithms. A discrete-event simulation model is developed to animate the stacking, retrieving, and reshuffling operations and to test the performance of the proposed heuristics and their extended versions in a dynamic environment with arrivals and retrievals of containers. The experimental results for the static problem show that the improved model can solve the reshuffling problem more quickly than the existing model and the proposed extended heuristics are superior to the existing ones. The experimental results for the dynamic problem show that the results of the extended versions of the five proposed heuristics are superior or similar to the best results of the existing heuristics and consume very little time

The synergistic effect of operational research and big data analytics in greening container terminal operations: a review and future directions

Container Terminals (CTs) are continuously presented with highly interrelated, complex, and uncertain planning tasks. The ever-increasing intensity of operations at CTs in recent years has also resulted in increasing environmental concerns, and they are experiencing an unprecedented pressure to lower their emissions. Operational Research (OR), as a key player in the optimisation of the complex decision problems that arise from the quay and land side operations at CTs, has been therefore presented with new challenges and opportunities to incorporate environmental considerations into decision making and better utilise the ‘big data’ that is continuously generated from the never-stopping operations at CTs. The state-of-the-art literature on OR's incorporation of environmental considerations and its interplay with Big Data Analytics (BDA) is, however, still very much underdeveloped, fragmented, and divergent, and a guiding framework is completely missing. This paper presents a review of the most relevant developments in the field and sheds light on promising research opportunities for the better exploitation of the synergistic effect of the two disciplines in addressing CT operational problems, while incorporating uncertainty and environmental concerns efficiently. The paper finds that while OR has thus far contributed to improving the environmental performance of CTs (rather implicitly), this can be much further stepped up with more explicit incorporation of environmental considerations and better exploitation of BDA predictive modelling capabilities. New interdisciplinary research at the intersection of conventional CT optimisation problems, energy management and sizing, and net-zero technology and energy vectors adoption is also presented as a prominent line of future research

Dynamics and equilibria under incremental horizontal differentiation on the Salop circle

We study product differentiation on a Salop circle when firms relocate incrementally due to bounded rationality. We prove that, under common assumptions on demand, firms relocate only when two or more firms target the same niche. In any other case, there is no incentive for any firm to relocate incrementally. We prove that all distributions in which firms are sufficiently far apart in product space are unstable Nash equilibria. We prove, in particular, that the classical equidistant distribution is an unstable Nash equilibrium that cannot emerge from another distribution. However, we show that if each firm is engaged in head-on rivalry with one other competitor, the industry converges to a ’equidistantesque’ equilibrium of clusters of rivals

The stochastic container relocation problem with flexible service policies

This paper investigates the Stochastic Container Relocation Problem in which a flexible service policy is adopted in the import container retrieval process. The flexible policy allows the terminal operators to determine the container retrieval sequence to some extent, which provides more opportunity for reducing the number of relocations and the truck waiting times. A more general probabilistic model that captures customers’ arrival preference is presented to describe the randomness for external truck arrivals within their appointed time windows. Being a multi-stage stochastic sequential decision-making problem, it is first formulated into a stochastic dynamic programming (SDP) model to minimize the expected number of relocations. Then, the SDP model is extended considering a secondary objective representing the truck waiting times. Tree search-based algorithms are adapted to solve the two models to their optimality. Heuristic algorithms are designed to seek high-quality solutions efficiently for larger problems. A discrete-event simulation model is developed to evaluate the optimal solutions and the heuristic solutions respectively on two performance metrics. Extensive computational experiments are performed based on instances from literature to verify the effectiveness of the proposed models and algorithms